Real, making their first appearance in the last eight since 2004, strolled past debutants Spurs after the 15th-minute dismissal of England striker Peter Crouch gave the home side's quest for a 10th European Cup crown a major boost.
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Jose Mourinho's side were already 1-0 up when Crouch earned a second booking after Adebayor had outjumped his marker at a fourth-minute corner and sent a downward header goalwards that neither keeper Heurelho Gomes nor Luka Modric on the line could keep out.
The Togo striker, on loan from Manchester City, added a second header in the 57th minute before Angel Di Maria scored the best goal of the night with a powerful shot into the top corner in the 72nd.
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Cristiano Ronaldo completed the rout in the closing stages with a fine volley from a Kaka cross as Real bounced back in style after Saturday's 1-0 home defeat by La Liga strugglers Sporting Gijon.
"Eleven against 10 at this level is mission impossible," said Mourinho who won the Champions League with Inter Milan last season and with Porto in 2004.
"I think Spurs will try everything in the second leg," the Portuguese told reporters. "They have belief and White Hart Lane is not an easy place to play.
"They will fight for sure. I know the mentality of English teams and their fans. We haven't lost yet in this season's Champions League so we'll try to get a positive result in London."
Adebayor, who had a spell with Tottenham's north London rivals Arsenal before joining City, has now scored 10 times against Spurs and was given a rapturous ovation when he was replaced by Gonzalo Higuain in the 75th minute.
BLISTERING TEMPO
A giant flag reading "To the final, let's go Madrid" and covering almost the entire first tier of the stands on one side of the stadium was unfurled before kickoff at the Bernabeu and Real began the game at a blistering tempo.
Around 3,000 Spurs fans high up in the stands were initially in excellent voice but their hopes of a surprise result in the Spanish capital were effectively dashed within a quarter of an hour.
After Adebayor had opened the scoring, Crouch lunged at Sergio Ramos in the eighth minute and was sent off after a similar challenge on Marcelo seven minutes later.
"I am disappointed. That was all we needed, going down to 10 men so early," said Spurs manager Harry Redknapp. "He (Crouch) shouldn't take that chance to make it a red c
